3d reconstruction method and 3d reconstruction system

ABSTRACT

A 3D reconstruction method for a thin film sample that includes a light element is provided. The method includes performing preprocessing that includes noise removal, field-of-view correction and background subtraction on original projection images captured by a scanning transmission electron microscope to obtain 2D images, performing several rounds of a 3D reconstruction procedure that includes an alignment process and an iterative algorithm based on the 2D images and reference images to obtain a piece of reconstructed 3D image data, generating a reconstructed 3D image related to the thin film sample based on the piece of reconstructed 3D image data, and displaying the reconstructed 3D image.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Taiwanese Invention PatentApplication No. 111113461, filed on Apr. 8, 2022.

FIELD

The disclosure relates to a three-dimensional (3D) reconstructiontechnique, and more particularly to a 3D reconstruction method and a 3Dreconstruction device for a thin film sample including a light element.

BACKGROUND

When using a transmission electron microscope to capture an image of athin film sample (e.g., a copolymer) that consists of light elements,such as hydrogen, carbon, nitrogen, oxygen, etc., the result may beunsatisfactory because contrast in the resulting images would not behigh enough. Therefore, the thin film sample is usually stained beforeimage capturing to enhance contrast. However, stains may interact withthe thin film sample and cause a structural change in the thin filmsample, so misjudgment might be made based on the resulting imagecaptured using this approach.

SUMMARY

Therefore, an object of the disclosure is to provide a three-dimensional(3D) reconstruction method and a 3D reconstruction device that areadapted for a thin film including a light element and that can alleviateat least one drawback of the prior art.

According to one aspect of the disclosure, the 3D reconstruction methodis to be implemented by a scanning transmission electron microscope(STEM) and a processor, and includes the following steps.

In one step, by the STEM, N number of original projection images of atarget area of the thin film sample are captured when the target area isat N number of different angles with respect to a horizontal plane,respectively, where N is a positive integer and the N number ofdifferent angles include a zero-degree angle, a plurality of positiveangles and a plurality of negative angles.

In one step, by the processor, preprocessing is performed on the Nnumber of original projection images to obtain N number oftwo-dimensional (2D) images that respectively correspond to the N numberof different angles, where the preprocessing includes noise removal,field-of-view correction and background subtraction.

In one step, by the processor, a 3D reconstruction procedure isperformed based on the N number of 2D images and N number of referenceimages that respectively correspond to the N number of different anglesto obtain a piece of reconstructed 3D image data related to the targetarea. The 3D reconstruction procedure includes:

-   -   for each of the N number of 2D images, performing an alignment        process on the 2D image so as to obtain an aligned 2D image that        corresponds to the respective one of the N number of different        angles, where the alignment process includes image shifting and        image rotation, the 2D image is shifted by a pixel shifting        amount that falls within a specific pixel range and rotated by        an angle rotating amount that falls within a specific angular        range to result in the aligned 2D image such that the aligned 2D        image has minimum error in terms of pixel values with respect to        the corresponding one of the N number of reference images, and        the pixel shifting amount and the angle rotating amount for each        of the N number of 2D images are recorded,    -   generating an initial 3D data distribution in reciprocal space        based on the aligned 2D images that respectively correspond to        the N number of different angles by using discrete Fourier        transform and interpolation,    -   combining the initial 3D data distribution and an arbitrary data        distribution to obtain a piece of 3D distribution data related        to the target area in the reciprocal space, where the arbitrary        data distribution is related to reciprocal lattice points in the        reciprocal space without the initial 3D data distribution,    -   performing an iterative algorithm based on the piece of 3D        distribution data to obtain a piece of iterative 3D distribution        data in the reciprocal space, the iterative algorithm including        performing inverse Fourier transform on the piece of 3D        distribution data to obtain a piece of 3D image data in real        space, extracting a 3D image data part that corresponds to the        target area from the piece of 3D image data, and performing        Fourier transform on the 3D image data part to obtain the piece        of iterative 3D distribution data,    -   substituting a piece of 3D data in the reciprocal space for a        data part of the piece of iterative 3D distribution data that        corresponds to the target area to obtain a piece of updated 3D        distribution data which serves as the piece of 3D distribution        data for a next round of the iterative algorithm, the piece of        3D data being obtained by performing Fourier transform on the N        number of 2D images,    -   repeating performing the iterative algorithm and substituting        the piece of 3D data until it is determined that an error        between the 3D image data part that was extracted in a latest        round of the iterative algorithm and the 3D image data part that        was extracted in a second latest round of the iterative        algorithm is smaller than a threshold value, and    -   making the 3D image data part that was extracted in the latest        round of the iterative algorithm serve as a piece of        reconstructed 3D image data that is obtained in this round of        the 3D reconstruction procedure.

In one step, by the processor, from the piece of reconstructed 3D imagedata, N pieces of 2D image data that respectively correspond to the Nnumber of different angles are extracted to serve as the N number ofreference images for a next round of the 3D reconstruction procedure.

In one step, by the processor, performing the 3D reconstructionprocedure and extracting the N pieces of 2D image data are repeateduntil it is determined that the pixel shifting amounts and the anglerotating amounts recorded for the N number of 2D images in a latestround of the 3D reconstruction procedure match the pixel shiftingamounts and the angle rotating amounts recorded for the N number of 2Dimages in a second latest round of the 3D reconstruction procedure.

In one step, by the processor, a reconstructed 3D image of the targetarea is generated based on the piece of reconstructed 3D image data thatwas obtained in the latest round of the 3D reconstruction procedure.

In one step, by the processor, a display device is controlled to displaythe reconstructed 3D image thus generated.

According to another aspect of the disclosure, the 3D reconstructionsystem includes a STEM, a storage device, a display device and aprocessor. The STEM includes a platform that is rotatable about an axis.The thin film sample is disposed on the platform and has a target areathat corresponds in position to the axis. The STEM is configured tocapture N number of original projection images of the target area whenthe target area is at N number of different angles with respect to ahorizontal plane, respectively, where N is a positive integer and the Nnumber of different angles include a zero-degree angle, a plurality ofpositive angles and a plurality of negative angles. The storage deviceis configured for data storage. The display device is configured forimage display. The processor is electrically connected to the STEM, thestorage device and the display device.

The processor is configured to receive the N number of originalprojection images from the STEM, and store the N number of originalprojection images in the storage device.

The processor includes a preprocessing module, an alignment module, aprocessing module, an iterative algorithm module, an iterativedetermination module, a reconstruction determination module and areconstruction module.

The preprocessing module performs preprocessing on the N number oforiginal projection images to obtain N number of two-dimensional (2D)images that respectively correspond to the N number of different angles.The preprocessing includes noise removal, field-of-view correction andbackground subtraction.

The processor performs a 3D reconstruction procedure based on the Nnumber of 2D images and N number of reference images that respectivelycorrespond to the N number of different angles to obtain a piece ofreconstructed 3D image data related to the target area.

During the 3D reconstruction procedure,

-   -   the alignment module, for each of the N number of 2D images,        performs an alignment process on the 2D image so as to obtain an        aligned 2D image that corresponds to the respective one of the N        number of different angles, where the alignment process that        includes image shifting and image rotation, the 2D image is        shifted by a pixel shifting amount that falls within a specific        pixel range and rotated by an angle rotating amount that falls        within a specific angular range to result in the aligned 2D        image such that the aligned 2D image has minimum error in terms        of pixel values with respect to the corresponding one of the N        number of reference images,    -   the alignment module, for each of the N number of 2D images,        records the pixel shifting amount and the angle rotating amount        in the storage device,    -   the processing module generates an initial 3D data distribution        in reciprocal space based on the aligned 2D images that        respectively correspond to the N number of different angles by        using discrete Fourier transform and interpolation,    -   the processing module combines the initial 3D data distribution        and an arbitrary data distribution to obtain a piece of 3D        distribution data related to the target area in the reciprocal        space, where the arbitrary data distribution is related to        reciprocal lattice points in the reciprocal space without the        initial 3D data distribution,    -   the iterative algorithm module performs an iterative algorithm        based on the piece of 3D distribution data to obtain a piece of        iterative 3D distribution data in the reciprocal space, where        the iterative algorithm includes performing inverse Fourier        transform on the piece of 3D distribution data to obtain a piece        of 3D image data in real space, extracting a 3D image data part        corresponding to the target area from the piece of 3D image        data, and performing Fourier transform on the 3D image data part        to obtain the piece of iterative 3D distribution data,    -   the iterative algorithm module substitutes a piece of 3D data in        the reciprocal space for a data part of the piece of iterative        3D distribution data that corresponds to the target area to        obtain a piece of updated 3D distribution data that serves as        the piece of 3D distribution data for a next round of the        iterative algorithm, where the piece of 3D data is obtained by        performing Fourier transform on the N number of 2D images and        being stored in the storage device,    -   the iterative algorithm module repeatedly performing the        iterative algorithm and substituting the piece of 3D data until        it is determined by the iterative determination module that an        error between the 3D image data part that was extracted in a        latest round of the iterative algorithm and the 3D image data        part that was extracted in a second latest round of the        iterative algorithm is smaller than a threshold value,    -   the iterative determination module makes the 3D image data part        that was extracted in the latest round of the iterative        algorithm serve as a piece of reconstructed 3D image data that        is obtained in this round of the 3D reconstruction procedure.

The processor is configured to extract, from the piece of reconstructed3D image data, N pieces of 2D image data that respectively correspond tothe N number of different angles to serve as the N number of referenceimages for a next round of the 3D reconstruction procedure.

The processor is configured to repeatedly perform the 3D reconstructionprocedure and extract the N pieces of 2D image data until it isdetermined by the iterative determination module that the pixel shiftingamounts and the angle rotating amounts recorded for the N number of 2Dimages in a latest round of the 3D reconstruction procedure match thepixel shifting amounts and the angle rotating amounts recorded for the Nnumber of 2D images in a second latest round of the 3D reconstructionprocedure.

The reconstruction module is configured to generate a reconstructed 3Dimage of the target area based on the piece of reconstructed 3D imagedata that was obtained in the latest round of the 3D reconstructionprocedure.

The processor is configured to control a display device to display thereconstructed 3D image thus generated.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the disclosure will become apparent inthe following detailed description of the embodiment(s) with referenceto the accompanying drawings, of which:

FIG. 1 is a block diagram illustrating a three-dimensional (3D)reconstruction system for a thin film sample including a light elementaccording to an embodiment of the disclosure;

FIG. 2 is a schematic diagram illustrating a scanning transmissionelectron microscopy according to an embodiment of the disclosure;

FIG. 3 is a flow chart illustrating a 3D reconstruction method accordingto an embodiment of the disclosure;

FIG. 4 is a flow chart illustrating sub-steps of a 3D reconstructionprocedure according to an embodiment of this disclosure;

FIG. 5 is a flow chart illustrating sub-steps of an iterative algorithmaccording to an embodiment of this disclosure;

FIG. 6 illustrates examples of original projection images and alignedtwo-dimensional (2D) images according to an embodiment of thisdisclosure; and

FIG. 7 illustrates examples of a theoretical structural model of a thinfilm sample and a reconstructed 3D image of the thin film sample.

DETAILED DESCRIPTION

Referring to FIG. 1 , a three-dimensional (3D) reconstruction system 100according to an embodiment of this disclosure is used to generate areconstructed 3D image of a thin film sample 200 (for example, acopolymer) that includes a light element (such as hydrogen, carbon,nitrogen, oxygen, or combinations thereof). The 3D reconstruction system100 includes a scanning transmission electron microscopy (STEM) 1, astorage device 2, a display device 3 and a processor 4 that iselectrically connected to the STEM 1, the storage device 2 and thedisplay device 3. In some embodiments, the storage device 2 is anon-volatile memory, the display device 3 is a screen, and the processor4 is a central processing unit. In some embodiments, the storage device2, the display device 3 and the processor 4 may be implemented by acomputer, such as but not limited to, a desktop computer, a notebookcomputer or a tablet computer.

Referring to FIG. 2 , the STEM 1 includes a platform 11 that isrotatable about an axis extending in a Y direction. The thin film sample200 is disposed on the platform 11 and has a target area correspondingin position to the axis, that is, a center of the target area isregistered to the axis. In this disclosure, when the platform 11 isparallel to a horizontal plane, an angle between the target area of thethin film sample 200 and the horizontal plane is zero degrees; when theplatform 11 is rotated in the clockwise direction from the perspectiveof FIG. 2 , an angle between the target area and the horizontal plane isdefined as a positive angle; when the platform 11 is rotated in thecounterclockwise direction from the perspective of FIG. 2 , an anglebetween the target area and the horizontal plane is defined as anegative angle. For example, the target area may be position at an anglewith respect to the horizontal plane ranging from about 70 degrees toabout −70 degrees. An X direction is on the horizontal plane andperpendicular to the Y axis. The STEM 1 emits an electron beam 12 in a Zdirection which is perpendicular to the X direction and the Y direction.The electron beam 12 passes through the target area of the thin filmsample 200 and the platform 11, and is detected by a STEM detector 13disposed underneath the platform 11 to obtain at least one originalprojection image.

The processor 4 includes a preprocessing module 41, an alignment module42, a processing module 43, an iterative algorithm module 44, aniterative determination module 45, a reconstruction determination module46 and a reconstruction module 47. In some embodiments, theaforementioned modules include software modular blocks that includeinstruction codes to be executed to carry out corresponding functionsdescribed in this disclosure. In some embodiments, the aforementionedmodules include hardware modules or circuits configured to carry out thecorresponding functions.

Referring to FIG. 3 , a 3D reconstruction method for a thin film sampleincluding a light element according to an embodiment of this disclosureis illustrated. The 3D reconstruction method is to be implemented by the3D reconstruction system 100 exemplarily shown in FIG. 1 , and includessteps S31 to S37.

In step S31, for image reconstruction of the target area of the thinfilm sample 200, the STEM 1 captures N number of original projectionimages of the target area when the target area is at N number ofdifferent angles with respect to the horizontal plane, respectively,where N is a positive integer and the N number of different anglesinclude an angle of zero degrees, a plurality of positive angles and aplurality of negative angles. For example, when N equals 25, twenty-fiveoriginal projection images of the target area at 60-degree angle,55-degree angle, . . . , 5-degree angle, 0-degree angle, −5-degreeangle, . . . , −55-degree angle and −60-degree angle are respectivelycaptured by the STEM 1, and the STEM 1 transmits the twenty-fiveoriginal projection images to the processor 4. Referring to FIG. 6 , aleft part of the figure exemplarily illustrates the twenty-five originalprojection images at the aforementioned twenty-five angles,respectively.

The processor 4 receives the N number of original projection images, andstores the same in the storage device 2.

In step S32, the preprocessing module 41 of the processor 4 performspreprocessing that includes noise removal, field-of-view correction andbackground subtraction on the N number of original projection images toobtain N number of two-dimensional (2D) images that respectivelycorrespond to the N number of different angles. Specifically, for eachof the N number of original projection images, the preprocessing module41 uses an algorithm of ensemble empirical mode decomposition to filterout noise so as to promote signal-to-noise ratio of the originalprojection image. Subsequently, the preprocessing module 41 performsfield-of-view correction with respect to the X direction on each of theoriginal projection images that has subjected to the noise removal. Insome embodiments, field-of-view correction is not required for theoriginal projection image that corresponds to the angle of zero degrees,and the field-of-view correction is performed based on a function X₀=X₀cos θ, where X₀ represents a corrected field of view in the X directionfor the original projection image that corresponds to an angle of θdegrees and X₀ represents a width in the X direction of the originalprojection image that corresponds to 0 degrees. Accordingly, for each ofthose of the original projection images subjected to the field-of-viewcorrection, only image data (e.g., pixel values) within the field ofview in the X direction are maintained, and image data outside the fieldof view are deleted. Lastly, the preprocessing module 41 performsbackground subtraction with respect to each of the original projectionimages that has undergone the noise removal and the field-of-viewcorrection, so as to obtain the N number of 2D images. In someembodiments, the 2D image that corresponds to the angle of zero degrees(referred to as “0-degree 2D image” hereinafter) is obtained based on anequation:

P _(bg) ⁰correct(x,y)=P _(raw) ⁰(x,y)−α₀×mean(P _(raw) ⁰(x,y)),

where P_(bg) ⁰ correct represents the 0-degree 2D image, P_(raw) ⁰represents the original projection image that corresponds to the angleof zero degrees after the noise removal, α₀ is decided in such a mannerthat image data corresponding to a background area of P_(raw) ⁰ (i.e.,an area not including a structure of the thin film sample 200) havemagnitudes greater than but substantially equal to zero, and x, yrespectively represent coordinates of an image. Similarly, the 2D imagethat corresponds to the angle of θ degrees (referred to as “θ-degree 2Dimage” hereinafter) is obtained based on an equation:

P _(bg) ^(θ)correct(x,y)=P _(raw) ^(θ)(x,y)−α_(θ)×mean(P _(raw)^(θ)(x,y)),

where P_(bg) ^(θ) correct represents the θ-degree 2D image, P_(raw) ^(θ)represents the original projection image that corresponds to the angleof θ degrees after the noise removal, α_(θ) is decided in such a mannerthat f^(θ)(y) and f⁰(y) have a minimum difference, f^(θ)(y) represents aone-dimensional function that is obtained by summing up all image dataof P_(bg) ^(θ)correct(x,y) in the X direction, and f⁰(y) represents aone-dimensional function that is obtained by summing up all image dataof P_(bg) ⁰correct(x,y) in the X direction.

In some embodiments, the preprocessing module 41 adjusts a center ofmass of the 0-degree 2D image to a center point of the 0-degree 2Dimage, and the center of mass located at the center point serves as anorigin of a coordinate system for the 0-degree 2D image.

In step S33, the processor 4 performs a 3D reconstruction procedurebased on the N number of 2D images and N number of reference images thatrespectively correspond to the N number of different angles (thereference image that corresponds to the angle of θ degrees beingreferred to as “θ-degree reference image” hereinafter) to obtain a pieceof reconstructed 3D image data related to the target area. Referring toFIG. 4 , the 3D reconstruction procedure includes sub-steps S41 to S47.

In sub-step S41, the alignment module 42, with respect to each of the Nnumber of 2D images, performs an alignment process on the 2D image so asto obtain an aligned 2D image that corresponds to the respective one ofthe N number of different angles (the aligned 2D image that correspondsto the angle of θ degrees being referred to as “θ-degree aligned 2Dimage” hereinafter). The alignment process includes image shifting andimage rotation. The 2D image is shifted in one direction by a pixelshifting amount that falls within a specific pixel range (for example,the 2D image that has 512×512 pixels may be shifted up, down, left orright by 50 pixels at the most (i.e., the specific pixel range is from 0to 50 pixels)) and rotated by an angle rotating amount that falls withina specific angular range (for example, the 2D image may be rotated inthe clockwise or counterclockwise direction by 3 degrees at the most(i.e., the specific angular range is from 0 to 3 degrees)) to result inthe aligned 2D image such that the aligned 2D image has minimum error interms of pixel values with respect to the corresponding one of the Nnumber of reference images. The processor 4 then records the pixelshifting amount and the angle rotating amount for each of the N numberof 2D images in the storage device 2.

In some embodiments, for the alignment process in a first round of the3D reconstruction procedure, the alignment module 42 performs thealignment process according to the following rules:

-   -   1. The 0-degree 2D image serves as the 0-degree reference image,        and is identical to the 0-degree aligned 2D image.    -   2. The alignment process is performed on the N number of 2D        images other than the 0-degree 2D image in an order from the 2D        image that corresponds to an angle with the smallest magnitude        to the 2D image that corresponds to an angle with the largest        magnitude.    -   3. For each of the N number of different angles other than the        zero-degree angle, the reference image that corresponds to this        angle is the aligned 2D image that corresponds to an adjacent        angle which is next to this angle and has a smaller magnitude        than this angle.

Following the aforementioned example where N equals 25 and thetwenty-five angles are the 60-degree angle, the 55-degree angle, . . . ,the 5-degree angle, the 0-degree angle, the −5-degree angle, . . . , the−55-degree angle and the −60-degree angle, the alignment module 42 makesthe 0-degree 2D image serve as the 5-degree reference image and the−5-degree reference image. Then, the alignment module 42 shifts the5-degree 2D image and the −5-degree 2D image by moving one pixel at atime, and compares these images after each movement with the 5-degreereference image and the −5-degree reference image, respectively, so asto obtain the pixel shifting amounts respectively for the 5-degree 2Dimage and the −5-degree 2D image that result in minimum differences withrespect to the 5-degree reference image and the −5-degree referenceimage, respectively. Next, the alignment module 42 rotates the 5-degree2D image and the −5-degree 2D image by rotating one degree at a time,and compares these images after each rotation with the 5-degreereference image and the −5-degree reference image, respectively, so asto obtain the angle rotation amounts respectively for the 5-degree 2Dimage and the −5-degree 2D image that result in minimum differences withrespect to the 5-degree reference image and the −5-degree referenceimage, respectively. Lastly, for each of the 5-degree 2D image and the−5-degree 2D image, the alignment module 42 shifts and rotates the 2Dimage by the corresponding pixel shifting amount and the correspondingangle rotation amount, respectively, in order to obtain thecorresponding one of the 5-degree aligned 2D image and the −5-degreealigned 2D image. The alignment module 42 further stores, for each ofthe 5-degree 2D image and the −5-degree 2D image, the correspondingpixel shifting amount and the corresponding angle rotation amount in thestorage device 2.

Similarly, the alignment module 42 makes the 5-degree aligned 2D imageand the −5-degree aligned 2D image serve as the 10-degree referenceimage and the −10-degree reference image, respectively. Then, thealignment module 42 shifts the 10-degree 2D image and the −10-degree 2Dimage by moving one pixel at a time, and compares these images aftereach movement with the 10-degree reference image and the −10-degreereference image, respectively, so as to obtain the pixel shiftingamounts respectively for the 10-degree 2D image and the −10-degree 2Dimage that result in minimum differences with respect to the 10-degreereference image and the −10-degree reference image, respectively. Next,the alignment module 42 rotates the 10-degree 2D image and the−10-degree 2D image by rotating one degree at a time, and compares theseimages after each rotation with the 10-degree reference image and the−10-degree reference image, respectively, so as to obtain the anglerotation amounts respectively for the 10-degree 2D image and the−10-degree 2D image that result in minimum differences with respect tothe 10-degree reference image and the −10-degree reference image,respectively. Lastly, for each of the 10-degree 2D image and the−10-degree 2D image, the alignment module 42 shifts and rotates the 2Dimage by the corresponding pixel shifting amount and the correspondingangle rotation amount, respectively, to obtain the corresponding one ofthe 10-degree aligned 2D image and the −10-degree aligned 2D image. Thealignment module 42 further stores, for each of the 10-degree 2D imageand the −10-degree 2D image, the corresponding pixel shifting amount andthe corresponding angle rotation amount in the storage device 2.

The alignment module 42 performs the alignment process on the remainderof the 2D images in a similar fashion to obtain the remainder of thealigned 2D images.

In sub-step S42, the processing module 43 generates an initial 3D datadistribution in reciprocal space (i.e., Fourier space) based on thealigned 2D images that respectively correspond to the N number ofdifferent angles by using discrete Fourier transform and interpolation.

In sub-step S43, the processing module 43 combines the initial 3D datadistribution and an arbitrary data distribution to obtain a piece of 3Ddistribution data that is related to the target area in the reciprocalspace, wherein the arbitrary data distribution is related to reciprocallattice points in the reciprocal space without the initial 3D datadistribution. In some embodiments, the arbitrary data distribution is aFourier transform of noise, and the initial 3D data distribution and thearbitrary data distribution may be in the form of functions while thepiece of 3D distribution data may be in the form of a matrix.

In sub-step S44, the iterative algorithm module 44 performs an iterativealgorithm based on the piece of 3D distribution data to obtain a pieceof iterative 3D distribution data in the reciprocal space. Referring toFIG. 5 , the iterative algorithm including sub-steps S51 to S53. Insub-step S51, the iterative algorithm module 44 performs inverse Fouriertransform on the piece of 3D distribution data to obtain a piece of 3Dimage data in real space. In sub-step S52, the iterative algorithmmodule 44 extracts a 3D image data part that corresponds to the targetarea from the piece of 3D image data. In sub-step S53, the iterativealgorithm module 44 performs Fourier transform on the 3D image data partto obtain the piece of iterative 3D distribution data.

In sub-step S45, the iterative algorithm module 44 substitutes a pieceof 3D data in the reciprocal space for a data part of the piece ofiterative 3D distribution data that corresponds to the target area toobtain a piece of updated 3D distribution data that serves as the pieceof 3D distribution data for a next round of the iterative algorithm. Insome embodiments, the piece of 3D data is obtained by the processingmodule 43 in advance by performing Fourier transform on the N number of2D images, and is stored by the processing module 43 in the storagedevice 2. Details regarding performing Fourier transform on the N numberof 2D images to obtain the piece of 3D data are similar to those asexplained in step S42, and are thus omitted herein for the sake ofbrevity.

In sub-step S46, the iterative determination module 45 determineswhether an error between the 3D image data part that was extracted in alatest round of the iterative algorithm and the 3D image data part thatwas extracted in a second latest round (i.e., the round immediatelyprior to the latest round) of the iterative algorithm is smaller than athreshold value. A flow of the 3D reconstruction procedure proceeds tosub-step S47 when it is determined that the error is smaller than thethreshold value; otherwise, the flow goes back to sub-step S44. In someembodiments, the error between the 3D image data part that was extractedin the latest round of the iterative algorithm and the 3D image datapart that was extracted in the second latest round of the iterativealgorithm is defined asError=Σ_(all voxel)|O(n)−O(n−1)|/Σ_(all voxel)O(n), where O(n)represents a function of the 3D image data part that was extracted inthe latest round of the iterative algorithm, and O(n−1) represents afunction of the 3D image data part that was extracted in the secondlatest round of the iterative algorithm. In some embodiments, thethreshold value is 1%.

It is noted that after the iterative algorithm module 44 performs afirst round of the iterative algorithm, since the round immediatelyprior to the first round does not exist, the flow directly goes back tosub-step S44 and then proceeds to sub-steps S45 and S46.

In other words, the iterative algorithm module 44 repeatedly performsthe iterative algorithm in sub-step S44 and the substituting of thepiece of 3D data in sub-step S45 until it is determined by the iterativedetermination module 45 that the error between the 3D image data partthat was extracted in the latest round of the iterative algorithm andthe 3D image data part that was extracted in the second latest round ofthe iterative algorithm is smaller than the threshold value.

In sub-step S47, the iterative determination module 45 makes the 3Dimage data part that was extracted in the latest round of the iterativealgorithm serve as a piece of reconstructed 3D image data that isobtained in this round of the 3D reconstruction procedure.

Referring once again to FIG. 3 , in step S34, the processing module 43of the processor 4 extracts, from the piece of reconstructed 3D imagedata obtained in step S33, N pieces of 2D image data that respectivelycorrespond to the N number of different angles to serve as the N numberof reference images for a next round of the 3D reconstruction procedure.

In step S35, the reconstruction determination module 46 of the processor4 determines whether the pixel shifting amounts and the angle rotatingamounts recorded for the N number of 2D images in a latest round of the3D reconstruction procedure match the pixel shifting amounts and theangle rotating amounts recorded for the N number of 2D images in asecond latest round of the 3D reconstruction procedure. A flow of the 3Dreconstruction method proceeds to step S36 when in the affirmative;otherwise, the flow goes back to step S33.

It is noted that after the processor 4 performs a first round of the 3Dreconstruction procedure, since the round immediately prior to the firstround does not exist, the flow directly goes back to step S33 and thenproceeds to steps S34 and S35.

In other words, the processor 4 repeats the 3D reconstruction procedurein step S33 and the extraction of the N pieces of 2D image data in stepS34 until it is determined that the pixel shifting amounts and the anglerotating amounts recorded for the N number of 2D images in the latestround of the 3D reconstruction procedure match the pixel shiftingamounts and the angle rotating amounts recorded for the N number of 2Dimages in the second latest round of the 3D reconstruction procedure. Inthis way, it can be assured that the N number of aligned 2D imagesobtained by performing the alignment process on the N number of 2Dimages in the latest round of the 3D reconstruction procedure areoptimum results. Referring to FIG. 6 , a right part of the figureillustrates the twenty-five aligned 2D images that respectivelycorrespond to the aforementioned twenty-five angles and that are optimumresults of the alignment process.

In step S36, the reconstruction module 47 of the processor 4 generates areconstructed 3D image of the target area based on the piece ofreconstructed 3D image data that was obtained in the latest round of the3D reconstruction procedure. It is noted that since the piece ofreconstructed 3D image data obtained in the latest round of the 3Dreconstruction procedure results from the optimum results of thealignment process, image resolution of the reconstructed 3D image may bepromoted.

In step S37, the processor 4 controls the display device 3 to displaythe reconstructed 3D image thus generated for viewing by technicians whoinspect and analyze the thin film sample 200.

FIG. 7 exemplarily illustrates a theoretical structural model of thethin film sample 200 (on the left side) and the reconstructed 3D imageof the thin film sample 200 generated by the 3D reconstruction methodaccording to an embodiment of this disclosure (on the right side).

To sum up, the original projection images of the target area of the thinfilm sample captured by the STEM are preprocessed to obtain the 2Dimages, and the 2D images undergo several rounds of the 3Dreconstruction procedure. Particularly, the preprocessing is able tomitigate issues of image deviation, image defects and other factors thatmay be unfavorable to 3D image reconstruction. Furthermore, in eachround of the 3D reconstruction procedure, the alignment process isperformed on the 2D images to result in the aligned 2D images and thealigned 2D images then undergo several rounds of the iterative algorithmso as to obtain the piece of reconstructed 3D image data for this roundof the 3D reconstruction procedure. Therefore, the reconstructed 3Dimage generated based on the piece of reconstructed 3D image data thatwas obtained in the latest round of the 3D reconstruction procedure canhave a relatively higher image resolution, in comparison to areconstructed 3D image that is generated directly based on the originalprojection images captured by the STEM. In addition, the thin filmsample no longer needs staining before image capturing, and a potentialstructural change in the thin film sample caused by stains can beprevented.

In the description above, for the purposes of explanation, numerousspecific details have been set forth in order to provide a thoroughunderstanding of the embodiment(s). It will be apparent, however, to oneskilled in the art, that one or more other embodiments may be practicedwithout some of these specific details. It should also be appreciatedthat reference throughout this specification to “one embodiment,” “anembodiment,” an embodiment with an indication of an ordinal number andso forth means that a particular feature, structure, or characteristicmay be included in the practice of the disclosure. It should be furtherappreciated that in the description, various features are sometimesgrouped together in a single embodiment, figure, or description thereoffor the purpose of streamlining the disclosure and aiding in theunderstanding of various inventive aspects, and that one or morefeatures or specific details from one embodiment may be practicedtogether with one or more features or specific details from anotherembodiment, where appropriate, in the practice of the disclosure.

While the disclosure has been described in connection with what is (are)considered the exemplary embodiment(s), it is understood that thisdisclosure is not limited to the disclosed embodiment(s) but is intendedto cover various arrangements included within the spirit and scope ofthe broadest interpretation so as to encompass all such modificationsand equivalent arrangements.

What is claimed is:
 1. A three-dimensional (3D) reconstruction methodfor a thin film sample that includes a light element, the 3Dreconstruction method to be implemented by a scanning transmissionelectron microscope (STEM) and a processor, and comprising: by the STEM,capturing N number of original projection images of a target area of thethin film sample when the target area is at N number of different angleswith respect to a horizontal plane, respectively, where N is a positiveinteger and the N number of different angles include a zero-degreeangle, a plurality of positive angles and a plurality of negativeangles; by the processor, performing preprocessing on the N number oforiginal projection images to obtain N number of two-dimensional (2D)images that respectively correspond to the N number of different angles,the preprocessing including noise removal, field-of-view correction andbackground subtraction; by the processor, performing a 3D reconstructionprocedure based on the N number of 2D images and N number of referenceimages that respectively correspond to the N number of different anglesto obtain a piece of reconstructed 3D image data related to the targetarea, the 3D reconstruction procedure including for each of the N numberof 2D images, performing an alignment process on the 2D image so as toobtain an aligned 2D image that corresponds to the respective one of theN number of different angles, where the alignment process includes imageshifting and image rotation, the 2D image is shifted by a pixel shiftingamount that falls within a specific pixel range and is rotated by anangle rotating amount that falls within a specific angular range toresult in the aligned 2D image such that the aligned 2D image hasminimum error in terms of pixel values with respect to the correspondingone of the N number of reference images, and the pixel shifting amountand the angle rotating amount for each of the N number of 2D images arerecorded, generating an initial 3D data distribution in reciprocal spacebased on the aligned 2D images that respectively correspond to the Nnumber of different angles by using discrete Fourier transform andinterpolation, combining the initial 3D data distribution and anarbitrary data distribution to obtain a piece of 3D distribution datarelated to the target area in the reciprocal space, the arbitrary datadistribution being related to reciprocal lattice points in thereciprocal space without the initial 3D data distribution, performing aniterative algorithm based on the piece of 3D distribution data to obtaina piece of iterative 3D distribution data in the reciprocal space, theiterative algorithm including performing inverse Fourier transform onthe piece of 3D distribution data to obtain a piece of 3D image data inreal space, extracting a 3D image data part that corresponds to thetarget area from the piece of 3D image data, and performing Fouriertransform on the 3D image data part to obtain the piece of iterative 3Ddistribution data, substituting a piece of 3D data in the reciprocalspace for a data part of the piece of iterative 3D distribution datathat corresponds to the target area to obtain a piece of updated 3Ddistribution data that serves as the piece of 3D distribution data for anext round of the iterative algorithm, the piece of 3D data beingobtained by performing Fourier transform on the N number of 2D images,repeating performing the iterative algorithm and substituting the pieceof 3D data until it is determined that an error between the 3D imagedata part that was extracted in a latest round of the iterativealgorithm and the 3D image data part that was extracted in a secondlatest round of the iterative algorithm is smaller than a thresholdvalue, and making the 3D image data part that was extracted in thelatest round of the iterative algorithm serve as a piece ofreconstructed 3D image data that is obtained in this round of the 3Dreconstruction procedure; by the processor, extracting, from the pieceof reconstructed 3D image data, N pieces of 2D image data thatrespectively correspond to the N number of different angles to serve asthe N number of reference images for a next round of the 3Dreconstruction procedure; by the processor, repeating performing the 3Dreconstruction procedure and extracting the N pieces of 2D image datauntil it is determined that the pixel shifting amount and the anglerotating amounts recorded for the N number of 2D images in a latestround of the 3D reconstruction procedure match the pixel shiftingamounts and the angle rotating amounts recorded for the N number of 2Dimages in a second latest round of the 3D reconstruction procedure; bythe processor, generating a reconstructed 3D image of the target areabased on the piece of reconstructed 3D image data that was obtained inthe latest round of the 3D reconstruction procedure; and by theprocessor, controlling a display device to display the reconstructed 3Dimage thus generated.
 2. The 3D reconstruction method as claimed inclaim 1, wherein, for the alignment process in a first round of the 3Dreconstruction procedure, the 2D image that corresponds to thezero-degree angle serves as the reference image that corresponds to thezero-degree angle, and is identical to the aligned 2D image thatcorresponds to the zero-degree angle, the alignment process is performedon the N number of 2D images other than the 2D image that corresponds tothe zero-degree angle in an order from the 2D image that corresponds toan angle with a smallest magnitude to the 2D image that corresponds toan angle with a largest magnitude, and for each of the N number ofdifferent angles other than the zero-degree angle, the reference imagethat corresponds to this angle is the aligned 2D image that correspondsto an adjacent angle which is next to this angle and has a smallermagnitude than this angle.
 3. The 3D reconstruction method as claimed inclaim 1, wherein: the error between the 3D image data part that wasextracted in the latest round of the iterative algorithm and the 3Dimage data part that was extracted in the second latest round of theiterative algorithm is defined asError=Σ_(all voxel)|O(n)−O(n−1)|/Σ_(all voxel)O(n), where O(n)represents a function of the 3D image data part that was extracted inthe latest round of the iterative algorithm, and O(n−1) represents afunction of the 3D image data part that was extracted in the secondlatest round of the iterative algorithm; and the threshold value is 1%.4. A three-dimensional (3D) reconstruction system for a thin film samplethat includes a light element, the 3D reconstruction system comprising:a scanning transmission electron microscope (STEM) that includes aplatform which is rotatable about an axis, the thin film sample beingdisposed on the platform and having a target area that corresponds inposition to the axis, the STEM being configured to capture N number oforiginal projection images of the target area when the target area is atN number of different angles with respect to a horizontal plane,respectively, where N is a positive integer and the N number ofdifferent angles include a zero-degree angle, a plurality of positiveangles and a plurality of negative angles; a storage device that isconfigured for data storage; a display device that is configured forimage display; and a processor that is electrically connected to theSTEM, the storage device and the display device; the processor isconfigured to receive the N number of original projection images fromthe STEM, and store the N number of original projection images in thestorage device; the processor including a preprocessing module, analignment module, a processing module, an iterative algorithm module, aniterative determination module, a reconstruction determination moduleand a reconstruction module; the preprocessing module is configured toperform preprocessing on the N number of original projection images toobtain N number of two-dimensional (2D) images that respectivelycorrespond to the N number of different angles, where the preprocessingincludes noise removal, field-of-view correction and backgroundsubtraction; the processor is configured to perform a 3D reconstructionprocedure based on the N number of 2D images and N number of referenceimages that respectively correspond to the N number of different anglesto obtain a piece of reconstructed 3D image data related to the targetarea; during the 3D reconstruction procedure, the alignment module, foreach of the N number of 2D images, performing an alignment process onthe 2D image so as to obtain an aligned 2D image that corresponds to therespective one of the N number of different angles, where the alignmentprocess includes image shifting and image rotation, the 2D image isshifted by a pixel shifting amount that falls within a specific pixelrange and is rotated by an angle rotating amount that falls within aspecific angular range to result in the aligned 2D image such that thealigned 2D image has minimum error in terms of pixel values with respectto the corresponding one of the N number of reference images, thealignment module recording, for each of the N number of 2D images, thepixel shifting amount and the angle rotating amount in the storagedevice, the processing module generating an initial 3D data distributionin reciprocal space based on the aligned 2D images that respectivelycorrespond to the N number of different angles by using discrete Fouriertransform and interpolation, the processing module combining the initial3D data distribution and an arbitrary data distribution to obtain apiece of 3D distribution data related to the target area in thereciprocal space, where the arbitrary data distribution is related toreciprocal lattice points in the reciprocal space without the initial 3Ddata distribution, the iterative algorithm module performing aniterative algorithm based on the piece of 3D distribution data to obtaina piece of iterative 3D distribution data in the reciprocal space, theiterative algorithm including performing inverse Fourier transform onthe piece of 3D distribution data to obtain a piece of 3D image data inreal space, extracting a 3D image data part that corresponds to thetarget area from the piece of 3D image data, and performing Fouriertransform on the 3D image data part to obtain the piece of iterative 3Ddistribution data, the iterative algorithm module substituting a pieceof 3D data in the reciprocal space for a data part of the piece ofiterative 3D distribution data that corresponds to the target area toobtain a piece of updated 3D distribution data that serves as the pieceof 3D distribution data for a next round of the iterative algorithm, thepiece of 3D data being obtained by performing Fourier transform on the Nnumber of 2D images and being stored in the storage device, theiterative algorithm module repeatedly performing the iterative algorithmand substituting the piece of 3D data until it is determined by theiterative determination module that an error between the 3D image datapart that was extracted in a latest round of the iterative algorithm andthe 3D image data part that was extracted in a second latest round ofthe iterative algorithm is smaller than a threshold value, the iterativedetermination module making the 3D image data part that was extracted inthe latest round of the iterative algorithm serve as a piece ofreconstructed 3D image data that is obtained in this round of the 3Dreconstruction procedure; the processor is configured to extract, fromthe piece of reconstructed 3D image data, N pieces of 2D image data thatrespectively correspond to the N number of different angles to serve asthe N number of reference images for a next round of the 3Dreconstruction procedure; the processor is configured to repeatedlyperform the 3D reconstruction procedure and extract the N pieces of 2Dimage data until it is determined by the iterative determination modulethat the pixel shifting amounts and the angle rotating amounts recordedfor the N number of 2D images in a latest round of the 3D reconstructionprocedure match the pixel shifting amounts and the angle rotatingamounts recorded for the N number of 2D images in a second latest roundof the 3D reconstruction procedure; the reconstruction module isconfigured to generate a reconstructed 3D image of the target area basedon the piece of reconstructed 3D image data that was obtained in thelatest round of the 3D reconstruction procedure; and the processor isconfigured to control the display device to display the reconstructed 3Dimage thus generated.
 5. The 3D reconstruction system as claimed inclaim 4, wherein, for the alignment process in a first round of the 3Dreconstruction procedure, the 2D image that corresponds to thezero-degree angle serves as the reference image that corresponds to thezero-degree angle, and is identical to the aligned 2D image thatcorresponds to the zero-degree angle, the alignment process is performedon the N number of 2D images other than the 2D image that corresponds tothe zero-degree angle in an order from the 2D image that corresponds toan angle with a smallest magnitude to the 2D image that corresponds toan angle with a largest magnitude, and for each of the N number ofdifferent angles other than the zero-degree angle, the reference imagethat corresponds to this angle is the aligned 2D image that correspondsto an adjacent angle which is next to this angle and has a smallermagnitude than this angle.
 6. The 3D reconstruction system as claimed inclaim 4, wherein: the error between the 3D image data part that wasextracted in the latest round of the iterative algorithm and the 3Dimage data part that was extracted in the second latest round of theiterative algorithm is defined asError=Σ_(all voxel)|O(n)−O(n−1)|/Σ_(all voxel)O(n), where O(n)represents a function of the 3D image data part that was extracted inthe latest round of the iterative algorithm, and O(n−1) represents afunction of the 3D image data part that was extracted in the secondlatest round of the iterative algorithm; and the threshold value is 1%.